Possible error in angular kinematics video

[moorepants]

"Furthermore, I noticed an error at minute 46:30 in the derivative of the angular velocity (a sin should be a cos)."

[moorepants]

I have this angular velocity:

$$ ^N \bar{\omega}^{B} = \dot{\beta}\hat{b}_x + \dot{\alpha}\sin\beta\hat{b}_y + \dot{\alpha}\cos{\beta}\hat{b}_z $$

The time derivative should be:

$$ ^N \bar{\alpha}^{B} = \ddot{\beta}\hat{b}_x + (\ddot{\alpha}\sin\beta) + \dot{\alpha}\cos{\beta}\dot{\beta})\hat{b}_y + (\ddot{\alpha}\cos{\beta} - \dot{\alpha}\sin{\beta}\dot{\beta})\hat{b}_z $$

[moorepants]

It is corrected in the handwritten notes.